Spontaneously established reverse electric field to enhance the performance of triboelectric nanogenerators via improving Coulombic efficiency

Mechanical energy harvesting using triboelectric nanogenerators is a highly desirable and sustainable method for the reliable power supply of widely distributed electronics in the new era; however, its practical viability is seriously challenged by the limited performance because of the inevitable side-discharge and low Coulombic-efficiency issues arising from electrostatic breakdown. Here, we report an important progress on these fundamental problems that the spontaneously established reverse electric field between the electrode and triboelectric layer can restrict the side-discharge problem in triboelectric nanogenerators. The demonstration employed by direct-current triboelectric nanogenerators leads to a high Coulombic efficiency (increased from 28.2% to 94.8%) and substantial enhancement of output power. More importantly, we demonstrate this strategy is universal for other mode triboelectric nanogenerators, and a record-high average power density of 6.15 W m−2 Hz−1 is realized. Furthermore, Coulombic efficiency is verified as a new figure-of-merit to quantitatively evaluate the practical performance of triboelectric nanogenerators.


Point-by-point responses to the reviewers' comments
We (the authors) would like to thank the editor and reviewers for dedicating their valuable time and expertise to assess the manuscript.We appreciate the reviewers' thorough and insightful comments, which significantly contributed to enhancing the quality of the present work.In the following we elucidate our response to each remark, along with the corresponding revisions made in the manuscript, in our pursuit of continued consideration for this submission.(Comments in Red, responses in Black, revisions in Blue.)

General remark
The manuscript reported a strategy to enhance the performance of TENGs by spontaneously established reverse electric field.It is a continuous work of a previous study (Nat Commun 14, 3218 (2023).https://doi.org/10.1038/s41467-023-38815-9) reported by the same group.Mechanisms reported here are similar to what was reported in the reported one.

Response
We are grateful for the reviewer's continuous attention of our group works, which is a great encouragement to us.
In 2019, our group firstly proposed the direct-current triboelectric nanogenerator (DC-TENG) based on triboelectrification and electrostatic breakdown (Sci.Adv. 5, eaav6437 (2019)).By placing an electrode on the side of the substrate, a fixed breakdown domain can be constructed between the charge collection electrode (CCE) and the triboelectric layer (TL) for electrostatic breakdown, and then a DC signal can be generated.
Previously, we assumed that the output performance of DC-TENG is decided only by one discharge domain-between the CCE and TL.However, it is difficult to explain experimental results such as the output charge decay at large external loads.Recently, we comprehensively analyzed the experimental and simulation results for DC-TENG (Nat. Commun.14, 3218 (2023).),and demonstrate that there are three breakdown domains: the first breakdown domain (1 st BD) between CCE and TL, the second breakdown domain (2 nd BD) between friction electrode (FE) and TL, and the third breakdown domain (3 rd BD) between CCE and FE (Figure R1).More importantly, we systematically imaged, defined, and regulated three discharge domains in DC-TENG, then a "cask model" was developed to bridge the cascaded-capacitor-breakdown dynamic model in the ideal condition and real outputs.
Although our previous work indicated that suppressing the electrostatic breakdown of 2 nd BD can improve the performance of DC-TENG, there are still no research on the following aspects: Comparing with the previous work, we report an important progress on these fundamental problems that the spontaneously established reverse electric field (SEREF) between the electrode and triboelectric layer restricts electrostatic breakdown by decreasing the electric field strength below critical breakdown electric field, which can be achieved by only pasting an insulator at the electrode edge.More importantly, the established electric field is selfregulation depending on the triboelectric charge density.Three unique capabilities of this strategy, which are not readily available in previous reports, have been demonstrated in this manuscript: 1.This strategy applies to both direct-current TENG (DC-TENG) based on electrostatic breakdown and alternatecurrent TENG (AC-TENG) based on electrostatic induction.With verified devices, the enhanced average power density of 2.30 W m -2 Hz -1 (increased by 54 times) in DC-TENG and a record-breaking average power density of 6.15 W m -2 Hz -1 (increased by 22 times) in AC-TENG strongly demonstrate the universality and effectiveness of the strategy.
2. This strategy is very simple to implement by just pasting a layer of insulation tape at the edge of the electrode, with the self-regulation behavior to adapt TENGs of different triboelectric charge density.
3. This strategy not only improves performance of TENG in the terms of Q SC and V OC like conventional strategies, but is also the first to improve performance from Coulombic efficiency.
Besides, a new figure-of-merit, Coulombic efficiency, is proposed and demonstrated for correctly quantifying the output performance of TENGs.Two unique characteristics of Coulombic efficiency compared with previous CMEO (the cycle for maximized energy output): 1. Coulomb efficiency proposed in this paper is not contradictory to CMEO.CMEO is more suitable for theoretical performance evaluation of TENG, and Coulomb efficiency also reflects the surface charge density decline degree dynamically caused by electrostatic breakdown, pointing out the direction for performance optimization of TENGs.
2. The Q-V (or I-V) curve of TENG drawn by Coulombic efficiency, V OC , and Q SC , as important as the I-V curve 3 / 37 for solar cells, can not only intuitively determine the performance of TENG, but also provide the most direct data reference for subsequent power management circuit design.
In addition to these we have reported in the manuscript, we also made the following supplements in the Supporting Information to further explain the difference in mechanism between the present work and the previous one.

Revisions
The revised part in the present manuscript is as follows: We have made a revision of "Although our previous work indicated that suppressing the electrostatic breakdown of 2 nd BD can improve the performance of DC-TENG (Supplementary Fig. 9) 28,29 ," in the second paragraph of "SEREF for regulating breakdown domains of DC-TENG".
The revised part in the present supplementary information is as follows: Previous work speculated that the insulator pasted at the edge of electrode was to completely replace the air in the 2 nd BD, increasing the breakdown threshold of 2 nd BD.Here, two experimental evidences indicate that it may be unreasonable.Firstly, when the insulator is nitrile, the effect of suppressing electrostatic breakdown is poor (Fig. 4eg).Furthermore, even in the presence of a minor air gap within the 2 nd BD, the effect of suppressing air breakdown still exists.These can be explained by the theory proposed in this work.

Response
We appreciate your professional review and reasonable suggestion.Given that TENG converts the mechanical energy in the periodic mechanical motion into electricity, its output power depends on the device area of TENG and the motion frequency 1,2 , so the power density is not an ideal parameter to assess the output capability of TENG.Energy density has been demonstrated as one of the most standardized parameters for TENG that is intrinsically not affected by the motion frequency.Here, the unit "W m -2 Hz -1 " can also be expressed as the energy density, i.e., "J m -2 ".Given that the power density at different frequencies is often obtained firstly, the unit "W m -2 Hz -1 " is widely used in many previous works for fair comparison.Therefore, we also use this unit to compare the output performance of our devices with the previous works.(Nat.Commun.

Remark-2
2) The max output power at a load of over several GΩ due to discharge was not an optimised parameter to characterize the TENG.Based on our experience, the power could be even higher if one has a higher load.Instead, the energy output would be a better parameter for comparison.

Response
We appreciate your professional review and reasonable suggestion.We will give a comprehensive analysis to show the similarity and difference of the maximum output power and maximum output energy.In our work, when measuring the optimal output power of TENG by changing the resistance, two possible results appeared as shown in Figure R3.One observation is that the output power reached its maximum value and then decreased as the resistance increases from several MΩ to several GΩ (Figure R3a-c), indicating a power inflection point; another observation is that the discharge signal occurs before the power inflection point (Figure R3d-f).In addition, other works about TENG's output power have also reported that the optimal resistance of TENG decreases with increasing motion frequency 3,4 , which can also be verified by TENG's theoretical capacitance model 5 .Indeed, this poses difficulty in comparing the performance of different TENGs.The above experimental results indicate that there is a certain similarity between the maximum output power of TENG measured by varying resistances and the maximum output energy measured by capacitances.We consider that the key point is not which method is more suitable for characterizing TENG's performance, but rather the specific conditions under which TENG can achieve its maximum output power/energy.This has been discussed in detail in this work.
We utilized the Coulomb efficiency proposed in this work, coupled with open-circuit voltage (V OC ) and short-circuit charge (Q SC ), to plot the Q-V curve of TENG.
The Q-V curve represents the output charge when the output voltage is V.The product of the horizontal and vertical coordinates of any points on the Q-V curve represents the output energy (E(V)) of TENG when the voltage is V.
Therefore, if the η(V OC ) ≤ 50%, the maximum output energy can be calculated as: In other words, TENG's output energy is maximum when the output voltage is V η = 50% (V η = 50% refers to the voltage corresponding to a Coulomb efficiency of 50%).

/ 37
When the η(V OC ) ≥ 50%, the maximum output energy can be calculated as: and TENG's output energy is maximum when the output voltage is close to V OC .
As shown in Figure R7 and Table R1, the η(V OC ) of the devices in Figure R3a-c (They are also the device 1#, device 2# and device 3# in Figure 3a.) is less than 50%, so there is a power/energy inflection point for these devices.The η(V OC ) of the devices in Figure R3d-f (They are also the device 4#, device 5# and device 6# in Figure 3a.) is greater than 50%, so there is no power/energy inflection point for these devices, leading to a higher output power or energy at the higher output voltage.In summary, the Coulombic efficiency we improved in this manuscript indicates that both power density and energy density are suitable for characterizing TENG's performance.For devices with the maximum output power inflection point, there is also a maximum output energy inflection point.The inflection point depends on the specific conditions under which TENG can achieve its maximum output power/energy.In comparison, testing the output energy of TENG can provide a more intuitive understanding of the relationship between TENG's output voltage and output energy.We have added Supplementary Figure 18 and Supplementary Note 6 in the supplementary information to introduce the method for measuring output energy of DC-TENG.In addition, we have added Supplementary Figure 19 and Supplementary Note 7 in the supplementary information to give a detailed analysis of maximum output power and output energy for TENG.

Revisions
The revised part in the present manuscript is as follows: We have made a revision of "Compared to the performance of DC-TENG without insulator (the gap of CCE and FE: 0.5 mm) and that of DC-TENG with insulator, Q SC keeps stable and V OC increases by 2.2 times, 4.2 times, and 5.9 times, and finally the average power has increased by 5.7 times, 7.9 times, and 10.7 times, respectively (Fig. 3a-c).
In addition, similar experimental phenomena arise during the testing of DC-TENG's output energy as well (Supplementary Fig. 18-19 and Supplementary Note 6-7)" in the last paragraph of "Performance enhancement of DC-TENG by SEREF".

The revised part in the present supplementary information is as follows:
Supplementary Note 6 The testing method for output energy of TENG The output energy of TENG for each motion cycle is not affected by the motion frequency.Here, the testing method for output voltage and Q-V curve of TENG proposed in this work is shown in Fig. 2g, which can also be utilized to measure the output energy of other TENGs (The schematic diagram of the testing circuit and the process of data processing are shown in Supplementary Fig. 18.).The output energy of TENG can be calculated based on the formula (E T = 0.5×C test ×(V n 2 -V n-1 2 ) (Supplementary Fig. 18b-d and Supplementary Fig. 18f-g).E T is the energy generated by TENG in each motion cycle, and V n is the voltage of C test (the testing capacitor) after the n th motion cycle.It is worth noting that when the voltage of C test reaches the breakdown threshold voltage of the 3 rd BD, discharge will occur and the energy stored in C test will stop to increase (Supplementary Fig. 18e and Fig. 2j-k).

Supplementary Note7 Comparison output power and output energy of TENG
Supplementary Fig. 19 shows the output energy of the six devices proposed in Fig. 3a.For the devices with the power inflection point (the device 1#, 2#, 3#), the highest output energy will be obtained at the intermediate motion cycle.For devices without the power inflection point (the device 4#, 5#, 6#), the energy in the last cycle is often the highest.The above experimental results indicate that there is a certain similarity between the maximum output power of TENG measured by varying resistances and the maximum output energy measured by capacitances.We consider that the key point is not which method is more suitable for characterizing TENG's performance, but rather the specific conditions under which TENG can achieve its maximum output power/energy.
According to Supplementary Note 10, it can be inferred that, if the η(V OC ) ≤ 50%, TENG's output energy is maximum when the output voltage is V η = 50% ; if the η(V OC ) ≤ 50%, TENG's output energy is maximum when the output voltage is close to V OC .As shown in Supplementary Fig. 25 and Supplementary Table 1, the η(V OC ) of the device 1#, device 2# and device 3# in Fig. 3a is less than 50%, so there is a power/energy inflection point for these devices.The η(V OC ) of the device 4#, device 5# and device 6# in Fig. 3a is greater than 50%, so the higher the output voltage, the greater the output power or energy for these devices.
In summary, the Coulombic efficiency we improved in this manuscript indicates that both power density and energy density are suitable for characterizing TENG's performance.For devices with maximum output power inflection point, there is also a maximum output energy inflection point.The inflection point depends on the specific conditions under which TENG can achieve its maximum output power/energy.In comparison, testing the output energy of TENG can provide a more intuitive understanding of the relationship between TENG's output voltage and output energy.

Remark-3
3) Although the performance has been improved by the strategy, the energy output was not impressive.Figure 2h shows an energy output of about 200 nC/s.

Response 11 / 37
We appreciate your professional review and generous comments.To measure the output charge of DC-TENG under different output voltage (V CCE-FE ), we designed a circuit as shown in Figure 2g (The detailed discussions are shown in Supplementary Note 5.).Figure 2h shows the charges stored in the C test of Figure 2g.The DC-TENG used in this experiment is the device 6# in Figure 3a.Comparing the performance of device 1# and 6# in Figure 3a, it can be observed that even though the short-circuit charge is consistent (Figure 3a), the output power increases from 58.4 μW to 630.7 μW (Figure 3c) due to different open-circuit voltage values (Figure 3b) and different Coulombic efficiencies (Supplementary Table 1).
It is worth noting that our strategy improving the performance of DC-TENG from three aspects: the output charge, the output voltage and Coulombic efficiency.Although the charge density in our work is not the highest reported value, enhancing V OC and Coulombic efficiency have enabled the highest output power density, demonstrating the effectiveness of our proposed strategy for performance optimization of TENG again.
For example, for the rotary mode DC-TENG in this work, the output charge density is 1.2 mC m -2 , while the highest output charge density of 8.8 mC m -2 has been reported in the microstructure-designed direct-current TENG (MDC-TENG) 6 .The output power density of DC-TENG designed by our strategy is 16-time of that of MDC-TENG (Figure 4k and Supplementary Note 11).For the sliding mode AC-TENG working in atmosphere conditions, the highest output charge density of 1.63 mC m -2 has been reported in the charge-space-accumulation sliding mode TENG (CAS-S-TENG) 7 , while the output charge density for the AC-TENG in this work is only 0.69 mC m -2 .However, the power density of our AC-TENG is up to 6.2 W m -2 Hz -1 , which is 5.7-time of that of CAS-S-TENG.These results indicate that output charge density is not the only parameter for evaluating and optimizing TENG performance.Therefore, we believe that the comprehensive enhancement in output charge, output voltage and Coulombic efficiency holds the key to further optimizing TENG's performance in the future.

Remark-4
4) It is strange to use Hz for the rotary system presented in Figure 4. Why not use rpm?

Response
We appreciate your professional review and reasonable suggestion.Generally, it is more appropriate to use the unit "rpm" for rotary systems rather than "Hz".Given the widespread adsorption of the unit "Hz" by various groups in numerous previous works (Nat.Commun.

Response
We appreciate your professional review and reasonable suggestion.We have provided a detailed description of the charge transfer mechanism in our manuscript and supplemented it with detailed schematic diagrams in the supporting information.

Revisions
The revised part in the present manuscript is as follows: We have made a revision of "Based on the triboelectrification effect between the friction electrode (FE) and triboelectric layer (TL), negative charges and positive charges are generated on the surface of TL and FE (Fig. 2a <i>).When DC-TENG moves left, a unidirectional electric field will be built between charge collection electrode (CCE) and TL to induce electrostatic breakdown, and negative charges transfer from the surface of TL to CCE driven by the Coulomb force; due to the significant potential difference between CCE and FE (Fig. 2a <ii> and Supplementary Fig. 8a), negative charges will transfer from CCE to FE, generating DC output in external circuit.
If the DC-TENG continues to move toward the left, a continuous DC output can be obtained.When DC-TENG moves right, the electric field between CCE and TL cannot induce electrostatic breakdown because the surface charge of TL below CCE is nearly zero (Fig. 2a <iii>); thus, there is no charge transfer between CCE and FE.The detailed schematic diagram of charge transfer in DC-TENG can also be found in many works (Supplementary Fig. 8b) 26,28 .

/ 37
The corresponding output charge and current is shown in Fig. 2b." in the first paragraph of "SEREF for regulating breakdown domains of DC-TENG".
We have added "

Remark-2
2. When the FE move from left to right there will be negative triboelectric charges on the TL (triboelectric layer) due to triboelectric effect which can create a negative potential on TL, hence a potential difference between FE and CCE.
In figure 2b, author has mentioned that there is no charge transfer between FE and CCE when sliding from right to left.Therefore, authors need to elaborate on how the charges transfer between FE and CCE for a whole unit cycle (right to left and left to right)?

Response
We appreciate your professional review and generous comments.We have made a clear description in the above answer.In short, when DC-TENG moves left, negative charge transfer from CCE to FE because of the potential difference between them (caused by electrostatic breakdown between CCE and TL); when DC-TENG moves right, there is no charge transfer between FE and CCE because of no potential difference between them (no electrostatic breakdown between CCE and TL).The detailed working mechanism can also be found in many previous works, and we also provide a detailed description of the charge transfer mechanism of DC-TENG in our manuscript and supplemented it with detailed schematic diagrams in the supporting information (Supplementary Fig. 8).

Remark-3
16 / 37 3.In Figure 3, authors have mentioned that Fig. 3b represents the Voc.If the V oc was measured between FE and CCE, this means that there is (theoretically) no charge transfer from FE to CCE.However, the graph shows that the V oc Increases with the increase of this gap between FE and CCE.Can the authors explain the reasons behind this?

Response
We appreciate your professional review and reasonable suggestion.We fully agree with your comment that "If the V oc was measured between FE and CCE, this means that there is (theoretically) no charge transfer from FE to CCE.".
We are very sorry for not clarifying the theoretical V OC and actual V OC in the previous manuscript.

For the theoretical V OC
Ideally, the open-circuit voltage (V OC ) of TENG can be calculated by the equation 5.
where Q SC is the short-circuit charges, and C T is the inherent capacitor of TENG (Supplementary Note 2).

For the achievable V OC in experiment
In actual conditions, the theoretical V OC generally cannot be obtained, which is mainly due to the unique working mechanism of TENG.On one hand, comparing with the large internal resistance and high voltage characteristics of TENG, the measurement instruments often fail to meet the requirements for the open-circuit condition.On the other hand, the unavoidable parasitic capacitance, the charge loss caused by electrostatic breakdown, and even the structural parameters will influence the achievable V OC in experiment, leading to the measured voltage significantly smaller than the theoretical V OC , which have been demonstrated in many previous works 8,9 .Therefore, the achievable V OC should be defined as the terminal voltage in the open-circuit state.Obviously, there is no charge transfer in external circuit in this state.

For the achievable V OC of DC-TENG
Given that the special structure and working mechanism of DC-TENG, the achievable V OC is more complex for different structures.In this work, the circuit for testing output voltage of TENG is shown in Figure 2g.As shown in Figure R11, for the DC-TENG with/without insulator, the output voltage fluctuates below a certain value due to the occurrence of 3 rd BD.This means that during this period (after output voltage reach this certain value) the charge transferred from DC-TENG to the C test is basically 0, which is very close to the open-circuit state that no charge transfer in external circuit, so we define the certain value as the V OC of DC-TENG.Obviously, the V OC of DC-TENG is equal to the breakdown threshold of 3 rd BD, and the observation experiment results (Figure R11c and Figure R11d) indicate that the spark discharge will cross the air gap between CCE and FE.Therefore, the larger the gap between CCE and FE or the wider the width of the insulator is, the higher the breakdown threshold of the 3 rd BD is, thus leading to a higher V OC .
In addition, to eliminate the possibility of the influence of the testing circuit on the experiment results, besides 17 / 37 conducting the leakage analysis experiment of the testing circuit mentioned in the present manuscript (Figure 2g and h), we also supplemented the experiment to analysis the influence of different testing capacitors on the experiment results (Figure R12).It is clearly that the achievable V OC is independent of the test capacitor, indicating that this voltage is the achievable maximum voltage for DC-TENG in experiment.We also added this part in the supplementary information to explain the definition of actual V OC and the difference between actual V OC and ideal V OC , and revised the part of Supplementary Note 5.

Revisions
The revised part in the present manuscript is as follows: output of each motion cycle of TENG.).Here, we discovered the surface charge and power loss resulting from electrostatic breakdown under load conditions, and proved that the slope of the V-Q curve remains constant while the curve itself collapses inward (The slope of the V-Q curve is the reciprocal of the inherent capacitance of the TENG.).
In response to this observation, we have made the following advancements in our manuscript.

A new mechanism for restricting electrostatic breakdown in TENGs
Conventional strategies restrict electrostatic breakdown by increasing the critical breakdown electric field of breakdown domain (the process 2 in Figure 1a and f), the new mechanism proposed in this paper modulates the electric field strength of breakdown domain below critical breakdown electric field by the spontaneously established reverse electric field (the process 3 in Figure 1a and f).This is completely different from the previous works and possesses merits of simple structure, self-regulation behavior and higher performance.

A simple and universal method for building the spontaneously established reverse electric field
The specific method explored in this paper is carried out by only pasting an insulator at the electrode edge, which is used to prevent charge leakage due to side-discharge flowing into the electrode, and to spontaneously accumulate static charges.Besides, benefited from the self-regulation of the spontaneously established reverse electric field (SEREF) (the self-regulation of SEREF refers as that the electric field strength of SEREF increases with output voltage or surface charge density), this method not only improves performance of TENG from Q SC and V OC , but is also the first to improve performance from Coulombic efficiency.

An unexpected and record-high output energy density
With the demonstration of DC-TENG devices, our strategy not only improves the short-circuit charge (Q SC ) and open-circuit voltage (V OC ), but also solves the issue of low charge utilization efficiency for the first time, and then a substantial enhancement of average power density of 2.3 W m -2 Hz -1 (increased by 54 times) is achieved owing to the improvement of Coulombic efficiency from 28.2% to 94.8%.For conventional AC-TENG, a record-breaking average power density of 6.15 W m -2 Hz -1 is also realized.

A new figure-of-merit for accurately evaluating the performance of TENG.
A new figure-of-merit, Coulombic efficiency, is proposed and demonstrated for correctly quantifying the output performance of TENGs, overcoming the issue of surface charge density decline dynamically caused by electrostatic breakdown.It provides a clear direction for guiding the design of high-performance TENGs and should be a standardized parameter for quantifying the performance of TENGs.

Huge potential for technology applications.
The performance of TENG can be further optimized by the synergetic enhancement of improved triboelectric charge critical breakdown electric field, which can be achieved by only pasting an insulator at the electrode edge (Supplementary Fig. 2b).
In addition, the high potential difference between nodes in the power management circuit can also cause electrostatic breakdown, thereby reducing the efficiency of power management circuits.This problem can be solved by encapsulating the power management module, such as circuit encapsulated in a highly insulating epoxy resin to prevent internal breakdown and leakage of electricity 1 .

Remark-3
High power management of the BEOL or interconnect technology is well-known in the semiconductor industry, and different techniques and proper design can be implemented to mitigate the early breakdown of the interconnect dielectrics.As an example, different automotive application implements 10kV signal in dielectrics of 10 -20 microns.
as a device for energy harvesting, using an additional voltage source to adjust the voltage applied to electrode B would be redundant for TENG.Therefore, we will try to achieve this objective through the design of the TENG, and we would like to express our gratitude to the reviewer again for the valuable comments.

Revisions
The revised part in the present manuscript is as follows: We have made a revision of "As shown in Fig. 1f, conventional strategies (increasing the threshold of electrostatic breakdown from E B1 to E B2 ) optimized TENG's performance from two aspects: Q SC or V OC .Our strategy focuses on modulating the electric field intensity in the breakdown domain by the SEREF, and comprehensively optimizes TENG's performance from three aspects: Q SC , V OC and Coulombic efficiency (η(V)), therefore the output energy can be greatly enhanced.The detailed discussions are shown in the following parts." in the first paragraph of "Discussion".
We have made a revision of "It is noteworthy that our strategy for modulating the electric field intensity to suppress electrostatic breakdown in the breakdown domain has not been previously reported in the research field of TENG.
Furthermore, we hypothesize that in addition to utilizing surface charge for electric field regulation, adjusting the terminal voltage of the electrode may also serve as a viable method (Supplementary Fig. 36 and Supplementary Note 13).More importantly, the performance of TENGs could be further optimized by the synergetic enhancement If increasing σ, increasing t or decreasing ε r , then the two curves intersect and air breakdown occurs.If decreasing σ, decreasing t or increasing decreasing ε r , then the two curves separate and air breakdown does not occur.
For the sliding mode TENG, the Paschen's law cannot be directly used for calculation, because of the non-ideal conditions.For example, the electric field around the sliding mode TENG is not uniform as assumed in Paschen's law, which depends on the mechanical configuration, triboelectric materials, surface roughness, and other issues.
Irrespective of the specific circumstance, there always exists a fixed breakdown threshold for the device that is fabricated (The breakdown could occur at the gap between the electrodes, the gap between the electrodes and the triboelectric layer, etc.).
Besides the demonstration methods in the original manuscript, we also provide another method to demonstrate the mechanism of discharge of sliding mode TENG.The device used in this experiment is the general sliding mode alternating current TENG (AC-TENG) (Figure R20a).The two bottom electrodes remain fixed, and the triboelectric layers are PVDF (polyvinylidene difluoride), PI (polyimide), ETFE (ethylene-terafluoroethlene), PTFE (Polytetrafluoroethylene), PVC (polyvinyl chloride) and FEP (fluorinated ethylene propylene), respectively.Firstly, we used the strategy proposed in this work to suppress side-discharge of electrodes (Figure R20b <i>) (Here, the insulating material is the same as the material of triboelectric layer to avoid triboelectrification between these two materials as much as possible.),and measured the surface charge density of triboelectric layer (the purple points in Figure R20c).Then, we removed the insulating material between the two bottom electrodes (Figure R20b <ii>), and measured the surface charge density of triboelectric layer again (the orange points in Figure R20c).It is obviously that the surface charge density of triboelectric layer decays to a low fixed value regardless of the triboelectric materials.These results demonstrate that the breakdown threshold is fixed when the device structure is determined again.

Figure R2 (Added Supplementary Figure 9 )
Figure R2 (Added Supplementary Figure 9).Experimental verification of the principle of suppressing electrostatic breakdown of pasting an insulator at the edge of FE in DC-TENG.(a) The structure diagram of DC-TENG without insulator.The gap between CCE and FE is 0.5 mm.(b) The structure diagram of DC-TENG with insulator.There is still about 0.4 mm of air gap in the 2 nd BD between CCE and FE.(c) The Q-V curve of DC-TENG.Previous work speculated that the insulator pasted at the edge of electrode was to completely replace the air in the 2 nd BD, increasing the breakdown threshold of 2 nd BD.Here, two experimental evidences indicate that it may be unreasonable.Firstly, when the insulator is nitrile, the effect of suppressing electrostatic breakdown is poor (Fig.4e-

Figure R3 (
Figure R3 (Revised Supplementary Figure 16).The output power of DC-TENG with different structure parameters.(a) <i> The structure diagram of DC-TENG without insulator.<ii> The output power of DC-TENG.The gap between CCE and FE is 0.5 mm.(b) <i> The structure diagram of DC-TENG without insulator.<ii> The output power of DC-TENG.The gap between CCE and FE is 1.0 mm.(c) <i> The structure diagram of DC-TENG without insulator.<ii> The output power of DC-TENG.The gap between CCE and FE is 2.0 mm.(d) <i> The structure diagram of DC-TENG with insulator.The width of insulator is 1.0 mm.<ii>The output power and <iii> the output voltage (The resistance is 4 GΩ.) of DC-TENG.(e) <i> The structure diagram of DC-TENG with insulator.The width of insulator is 2.0 mm.<ii> The output power and <iii> the output voltage (The resistance is 7 GΩ.) of DC-TENG.(f) <i> The structure diagram of DC-TENG with insulator.The width of insulator is 3.0 mm.<ii> The output power and <iii> the output voltage (The resistance is 20 GΩ.) of DC-TENG.Obviously, when a breakdown signal occurs in the current signal, the corresponding output voltage approaches the threshold voltage of the 3 rd BD (i.e. the open circuit voltage of DC-TENG).

Figure R4 (
Figure R4 (Added Supplementary Figure 18).The testing method for output energy of TENG.(a) The schematic diagram of the testing circuit.<i> When the DC-TENG moves left, current flows from FE to CCE and charge is stored in the testing capacitor (C test ).<ii> When the DC-TENG moves right, current is zero.Rp is a protective resistor, which is utilized to protect the charge meter.(b)-(d) The schematic diagram of testing output energy for DC-TENG.The green/orange/purple shadow area represent the output energy of DC-TENG in the 1 st /2 nd /3 rd motion cycle.Q n is the total output charge after the n th motion cycle.Q n -Q n-1 is the output charge of the n th motion cycle.V n is the output voltage after the n th motion cycle.(e) The output charge and output voltage of DC-TENG (Without insulator, the gap between CCE and FE is 0.5 mm.).(f)-(g) The output energy of DC-TENG in the n th motion cycle (Without insulator, the gap between CCE and FE is 0.5 mm.).

Figure R5 (
Figure R5 (Figure 2j-k).(a) The output voltage of DC-TENG without insulator.(b) The output voltage of DC-TENG with insulator.Inset figures of (a) and (b) are the photos of spark discharge of 3 rd BD (Scale bar: 5 mm).

Figure R7 (
Figure R7 (Revised Supplementary Figure 25).The Q-V curve of DC-TENGs with different structure parameters obtained by linearly fitting the experimental data.(a) The Q-V curve of DC-TENG without insulator.<i>-<iii> The gap between FE and CCE is 0.5 mm, 1.0 mm and 2.0 mm, respectively.The detailed structure diagram is shown in Supplementary Fig.16a-c.(b) The Q-V curve of DC-TENG with insulator.<i>-<iii> The width of insulator is 1.0 mm, 2.0 mm and 3.0 mm, respectively.The detailed structure diagram is shown in Supplementary Fig.16d-f.The Coulombic efficiency of these devices is shown in Supplementary Table1.

28 .
Figure R10 (Revised Supplementary Figure 8).The detailed mechanism for DC-TENG.(a) The simulated result of the potential difference between CCE and FE.Obviously, the potential of FE is higher than that of CCE, thus negative charges transfer from CCE to FE.(b) The detailed charge transfer mechanism for DC-TENG.

Figure R11 (
Figure R11 (Added Supplementary Figure 13.).The breakdown threshold of 3 rd BD.(a) The output voltage of DC-TENG without insulator.(b) The output voltage of DC-TENG with insulator.The output voltage of DC-TENG will no longer over the certain value due to the occurrence of 3 rd BD.(c) and (d) are the photos of spark discharge of 3 rd BD (Scale bar: 5 mm).

Figure R12 (
Figure R12 (Added Supplementary Figure 12.).The output voltage of DC-TENG when the C test is different.The experimental results indicate that C test has no effect on the 3 rd BD of DC-TENG.

Figure R14 (
Figure R14 (Added Supplementary Figure 1).The power management of TENG.(a) The represented power management circuit.(b) The output power of DC-TENG with different output voltage with/without power management circuit.The DC-TENG used in this experiment is shown in Fig. 4h.C in is 55 pF, which is obtained by connecting four 220 pF capacitors in series.The threshold voltage of gas discharge tube (GDT) is 1500 V.The reverse breakdown voltage of freewheeling diode is 2000 V. L is 330 μH.C out is 10 μF.

Figure R15 (Added Supplementary Figure 2 )
Figure R15 (Added Supplementary Figure 2).The output charge of DC-TENG when the potential at node A increases.(a) The test circuit.The potential at node A can be controlled by changing the output voltage of the voltage source.(b) The output charge of DC-TENG.The DC-TENG used in this experiment is shown in Fig. 2j and 2k.

Figure R16 (
Figure R16 (Added SupplementaryFigure36).The simulated electric field around the edge of electrode (surface charge density of the triboelectric layer is -50 μC m -2 .).E2 is used to modulate the electric field.The insulator between electrodes is mainly used for electrode isolation.<i>-<iv> As the voltage applied to E2 increases from zero to -500 V, the region of the breakdown domain gradually decreases.The data in (b) is taken from the electric field intensity at 5 μm above the triboelectric layer in (a).

Figure R19 (
Figure R19 (Added Supplementary Figure 34).The breakdown theory of CS-TENG.(a) The structure diagram of CS-TENG.V air is the air gap voltage of CS-TENG.σ is the surface charge density of triboelectric layer.t and ε r are the thickness and relative dielectric constant of triboelectric layer, respectively.ε 0 is 8.85×10 -12 F m -1 .(b)The relationship between V b curve (the orange line) and V air (the blue lines).When σ is 250 μC m -2 , t is 50 μm, ε r is 2.1, air breakdown does not occur due to two curves are tangent, and 250 μC m -2 is the maximum surface charge density.If increasing σ, increasing t or decreasing ε r , then the two curves intersect and air breakdown occurs.If decreasing σ, decreasing t or increasing decreasing ε r , then the two curves separate and air breakdown does not occur.

Figure R21 (
Figure R21 (Added SupplementaryFigure10).The cross section of the DC-TENG.<i> The structure diagram of DC-TENG (a) without insulator, (b) with insulator.The purple shaded area is the observation area.<ii> SEM image of the observed area (scale bar: 200 μm).<iii> The distribution of elements at the observation area of DC-TENG was analyzed by using the energy-spectrum scanning function of SEM.The yellow dots represent copper element, green dots represent carbon element.Due to the devices are handmade and the cross section is relatively rough, it is difficult to distinguish the positional relationship between electrodes and insulator solely based on SEM images.Therefore, we have supplemented the element distribution at the observation area.Due to the substrate of the device is acrylic (Polymeric Methyl Methacrylate, PMMA) and the insulation layer is polyimide (PI), their main element is carbon and does not contain copper.The main element of the electrode is copper and does not contain carbon.Therefore, the electrodes and insulator can be distinguished by analyzing the distribution of carbon and copper elements at the observation area.

Table 8 . Supplementary Table 4 . The detailed parameters of different rotation mode DC-TENGs.
detailed motion parameters of our devices.We added this part as Supplementary Table4in the supplementary information, revised Figure4iin manuscript and Supplementary Fig.29bin Supplementary information.In addition, we also added the detailed motion parameters of our devices in Supplementary

Table 8 . The detailed motion parameters of sliding-mode TENG Parameters Device Acceleration Deceleration Maximum rate Frequency Distance Pressure
Remark-11.Author should provide clarifications on how charges move from FE (Friction electrode) to charge collecting electrode (CCE).The potential difference graph is given in the paper; however, a suitable description should also be study https://doi.org/10.1021/acsnano.0c00138 for example, which contains such a description.